The last decade witnessed an explosion in the availability of data for
operations research applications. Motivated by this growing availability, we
propose a novel schema for utilizing data to design uncertainty sets for robust
optimization using statistical hypothesis tests. The approach is flexible and
widely applicable, and robust optimization problems built from our new sets are
computationally tractable, both theoretically and practically. Furthermore,
optimal solutions to these problems enjoy a strong, finite-sample probabilistic
guarantee. \edit{We describe concrete procedures for choosing an appropriate
set for a given application and applying our approach to multiple uncertain
constraints. Computational evidence in portfolio management and queuing confirm
that our data-driven sets significantly outperform traditional robust
optimization techniques whenever data is available.Comment: 38 pages, 15 page appendix, 7 figures. This version updated as of
Oct. 201